max taldykin
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 Dec19 awarded Caucus Sep1 comment Constructive proof of pigeonhole principle Sorry for delay. I just completed the proof, you can see it here. It is still hairy and badly structured. I'll try to simplify it and then will post it here as a separate answer. Thanks again for the detailed explanation. Aug27 comment Constructive proof of pigeonhole principle I succeeded formalizing everything except $(\forall f)(\forall k)(\forall m)[(\exists i < m)[f(i) = k] \lor \lnot (\exists i < m)[f(i) = k]]$. It is easy to prove it by classic axiom but I still trying to understand how to prove it by induction. Aug27 accepted Constructive proof of pigeonhole principle Aug27 comment Constructive proof of pigeonhole principle I'll try to formalize this proof an then will accept your answer. Aug27 comment Constructive proof of pigeonhole principle Thank you very much. The proof is really easy and straightforward, I even thought about applying inductive hypothesis to some new function but then got distracted and switched to googling for hints. Aug27 comment Constructive proof of pigeonhole principle Yep, sorry. I added my definition (failed to TeXify it, but hope it is clear as it is). Aug27 revised Constructive proof of pigeonhole principle added 216 characters in body Aug27 asked Constructive proof of pigeonhole principle May15 awarded Caucus Nov27 comment Expected value of minimum distance I need some time to understand this but accepting it for now. Thanks for answering. Nov27 accepted Expected value of minimum distance Nov27 comment Expected value of minimum distance @Yury, Wow. Can you please post this as an answer with little more explanations? Nov27 comment Expected value of minimum distance @Yury, I think we can assume only $n > m$ not $n >> m$. But if this somehow simplifies solution, you are welcome: solution to some similar problem is better than no solution at all. Nov27 comment Expected value of minimum distance @mike, thanks. reading about order stats now, seems relevant. Nov27 comment Expected value of minimum distance @Henry, yes integers are not necessarily distinct Nov27 comment Expected value of minimum distance @Yury, closed form is preferable Nov26 awarded Commentator Nov26 awarded Editor Nov26 comment Expected value of minimum distance @user1551, fixed, thanks for pointing.